Kyle Weaver made two free throws with :46 seconds to play, but the Cats struck quickly when Budinger nailed a three just seven seconds later.
The Cats quickly fouled but Robbie Cowgil only made one of two foul shots and the Cats struck quickly again with a Marcus Williams lay-in.
Again the Wildcats fouled, but this time Kyle Weaver missed bouth foul shots and Ivan Radenovic nailed a three pointer from the top of the key to tie things up with :16 left.
Arizona actually had a chance to win in regulation after Derrick Low was called for an offensive foul with eight seconds to play, but the Wildcats took too long to set up and Radenovic had to rush a shot at the buzzer that was off target.
The overtime session was similar except the Wildcats were unable to battle back.
The Cougars scored the first six of the extra session but the Cats answered with four in a row to cut the score to 73-71.
The Cougars went up 77-71, but Shakur made a lay-in to cut it to four, and Daven Harmeling missed both free throws, but the Cats took too long to get off a final shot and killed any chance at getting the necessary possessions to come back.
The Cougars were led by Harmeling who hit seven three pointers.
Shakur led the Wildcats with 19 points, eight rebounds and eight assists.
All told the Cats shot just 39.4% from the field and were a paltry 6-21 from behind the arc.
Frankly the Cats looked tired, both mentally and physcally tired. They only committed 13 turnovers, but had several passes tipped or mishandled that kept the Wildcats out of their offensive flow.
Marcus Williams scored 19 points and grabbed nine rebounds. Ivan Radenovic scored 17 points and had eight rebounds.
The Cats saw their 12-game win streak snapped and fell to 3-1 in conference.